Problem: $A$ $B$ $C$ If: $ BC = 7x + 7$, $ AB = 9x + 4$, and $ AC = 59$, Find $BC$.
Solution: From the diagram, we can see that the total length of ${AC}$ is the sum of ${AB}$ and ${BC}$ $ {AB} + {BC} = {AC}$ Substitute in the expressions that were given for each length: $ {9x + 4} + {7x + 7} = {59}$ Combine like terms: $ 16x + 11 = {59}$ Subtract $11$ from both sides: $ 16x = 48$ Divide both sides by $16$ to find $x$ $ x = 3$ Substitute $3$ for $x$ in the expression that was given for $BC$ $ BC = 7({3}) + 7$ Simplify: $ {BC = 21 + 7}$ Simplify to find ${BC}$ : $ {BC = 28}$